# Physics

One end of a rubber band with a length L is attached to a wall. The rubber band is held horizontally and the loose end is pulled away from the wall at a speed v, stretching the band. Simultaneously, an ant begins to crawl away from the wall along the rubber band with a speed u < v. Assume that the rubber band can be infinitely stretched. Will the ant ever make it to the loose end of the rubber band? If so, how long will it take?

The speed of the ant is u+ speed of band. The speed of the band depends on where the ant is, at the end it is v, halfway it is v/2, and at position d from the wall it is d*v/(L+v*time)

So to get to the end, the ant has to go faster than the band below him. He is, because u+ d*v/(v*time)>velocity of band below him.

consider The position of the ant at time T.
Position= average velocity*Time
= [u + 1/2 (position*v/(v*T)*]T
=uT + 1/2 *position*vT/(VT)

solving this for position...
Position = uT/[1-vt/2(vT)]=2 uT
So, can position of the ant ever be greater than vT , the end of the band...
vT =? 2uT so it can be true if

u = v/2 or greater.

I have an error I forgot to delete... Here is the new..
The speed of the ant is u+ speed of band. The speed of the band depends on where the ant is, at the end it is v, halfway it is v/2, and at position d from the wall it is d*v/(L+v*time). This assumes constant velocity v for the end of the rubber band.(Acceleration is zero)

So to get to the end, the ant has to go faster than the band below him. He is, because u+ d*v/(v*time)>velocity of band below him.

consider The position of the ant at time T.
Position= average velocity*Time
= [u + 1/2 (position*v/(v*T)*]T
=uT + 1/2 *position*vT/(VT)

solving this for position...
Position = uT/[1-vt/2(vT)]=2 uT
So, can position of the ant ever be greater than vT , the end of the band...
vT =? 2uT so it can be true if

u = v/2 or greater.

1. 👍
2. 👎
3. 👁

## Similar Questions

1. ### Math

A box contains 95 pink rubber bands and 90 brown rubber bands. You select a rubber band at random from the box. Find each probability. Write the probability as a fraction in simplest form. a. Find the theoretical probability of

A box contains 95 pink rubber bands and 90 brown rubber bands. You select a rubber band at random from the box. Find each probability. Write the probability as a fraction in simplest form. a. Find the theoretical probability of

3. ### Physics

A uniform beam of length 1.0 m and mass 16 kg is attached to a wall by a cable that makes an angle of 30 degrees with the end of the beam, as shown in the figure. The beam is free to pivot at the point where it attaches to the

4. ### Physics

A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of mb = 6.7 kg and the sign has a mass of ms = 17.4 kg. The length of the beam is L = 2.83 m. The sign is attached at the very end of the beam, but the

1. ### Physics! plese help

A 1320-N uniform beam is attached to a vertical wall at one end and is supported by a cable at the other end. A 1960-N crate hangs from the far end of the beam. Using the data shown in the figure, find (a) the magnitude of the

2. ### Physics

A 500N person stands 2.5m from a wall against which a horizontal beam is attached. The beam is 6m long and weighs 200N. A cable is attached to the free end of the beam and makes an angle of 45 to the horizontal and is attached to

3. ### Physics

When the rubber band in a slingshot is stretched, it obeys Hooke's law. Suppose that the "spring constant" for the rubber band is k = 44.2 N/m. When the rubber band is pulled back with a force of 9.38 N, how far does it stretch?

4. ### physics

A rubber band has a"spring constant" of 45 N/m. When the rubber band is pulled by a force of 9.8 N , how far will it stretch and what is potential energy?

1. ### Physics

A force of 2N will stretch a rubber band 2 cm. Assuming that Hooke's law applies, how far will a 4N force stretch the rubber band? How much work does it take to stretch the rubber band this far?

2. ### Physics

The unstretched length of a piece of elastic rubber is 5cm a force of 9N is required to stretch if by 1cm.what amount of work will be done to stretch the rubber from a length of 12cm to 8cm if the rubber remained within the

3. ### physics

A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of mb = 6.9 kg and the sign has a mass of ms = 15.3 kg. The length of the beam is L = 2.55 m. The sign is attached at the very end of the beam, but the

4. ### physics!

A stretched rubber band has a length of 0.10m and a fundamental frequency of 440Hz. What is the speed at which waves travel on the rubber band? I need some ideas to do this problem. Thanks!